Momentum: MACD Spread¶

2023-02-21.

Summary¶

We test a systematic strategy based on a spread variation of the Moving Average Convergence / Divergence (MACD) indicators on a BTC/USD portfolio.

Hypothesis: Rebalancing portfolio on MACD spread on tiered overbought/oversold signals performs better on a risk-adjusted basis than holding BTC over certain periods.

Parameters:

Date: 2011-02-10 to 2023-02-09
Frequency: daily
No additional buy in after Time 0
No trading fees
No shorting

Findings:

Overall, MACD spread portfolio results in lower annualized Sharpe Ratio generally (excl. rf, both simple and log returns) than holding
In few cases, portfolio outperforms holding in non-annualized and annualized Sharpe Ratio

Discussion -> Next Steps:

Strategy missed ~first half of 2017 bull run -> perhaps overtuned to avoid bear runs, alternatives: adjust tiers, buy cheap puts while holding
Need to backtest over training / testing data

1. Data¶

1.1. Import¶

Market Data as of: 2023-02-10
BTC price data: Coin Metrics 'ReferenceRateUSD'
SPY price data: WSJ Market Data

	btc
time
2009-01-03	0.000000
2009-01-04	0.000000
2009-01-05	0.000000
2009-01-06	0.000000
2009-01-07	0.000000
...	...
2023-02-05	23355.524386
2023-02-06	22957.225191
2023-02-07	22745.165037
2023-02-08	23266.269204
2023-02-09	22937.579945

5151 rows × 1 columns

	btc
count	5151.000000
mean	7756.203500
std	13940.029711
min	0.000000
25%	11.052683
50%	589.373502
75%	8795.111442
max	67541.755508

	Open	High	Low	Close	Volume
Date
2010-12-29	125.98	126.20	125.9000	125.92	58033039
2010-12-30	125.80	126.13	125.5300	125.72	76616852
2010-12-31	125.53	125.87	125.3300	125.75	91270273
2011-01-03	126.71	127.60	125.6969	127.05	138725203
2011-01-04	127.33	127.37	126.1900	126.98	137409703
...	...	...	...	...	...
2023-02-03	411.59	416.97	411.0900	412.35	94736781
2023-02-06	409.79	411.29	408.1000	409.83	60295328
2023-02-07	408.87	416.49	407.5700	415.19	90990750
2023-02-08	413.13	414.53	409.9300	410.65	76227453
2023-02-09	414.41	414.57	405.8100	407.09	78694867

3050 rows × 5 columns

	Open	High	Low	Close	Volume
count	3050.000000	3050.000000	3050.000000	3050.000000	3.050000e+03
mean	251.600702	253.000111	250.076330	251.637781	1.104180e+08
std	95.916431	96.577802	95.175804	95.917162	6.411999e+07
min	108.350000	112.580000	107.430000	109.930000	2.027001e+07
25%	181.357500	182.102250	180.807500	181.591250	6.824341e+07
50%	226.875000	227.780000	226.140000	227.075000	9.334451e+07
75%	303.460000	306.201250	300.665000	303.322500	1.340440e+08
max	479.220000	479.980000	476.060000	477.710000	7.178286e+08

1.2. Analysis¶

We observe that BTC historical price movement is exponential relative to the SPY as benchmark. Logging BTC price is warranted for strategies.

BTC's 1yr trailing correlation with SPY is around 0.15. It is higher under 90d trailing and 30d trailing, reaching at peaks around 0.38 and 0.6 historically.

Further, we see from the histogram and more clearly QQ plot that historical BTC returns distribution is far less normally distributed compared to SPY with long tail returns.

High volatility and exponential price movement make moving averages, and momentum strategies in general, less applicable to BTC due to their reliance on smoothing over historical trailing periods. Further, annualizing Sharpe ratio from daily returns is less applicable due to particularly evident violation of IID. Preliminary analysis suggests momentum might not outperform holding, and that exponential moving averaging should outperform simple moving averaging.

2. Create Signals¶

2.1. Define Variables¶

The standard MACD Logic is as follows:

MACD line = 12d price EMA - 26d price EMA
Signal line = 9d MACD EMA
Long: MACD line - Signal line > 0 (cross over)
Short/sell: MACD line - signal line < 0 (cross under)

We make the following adjustments:

Use SMA instead of EMA
MACD spread = 26d overbought/oversold SMA z scores
Long: MACD spread < z score threshold (oversold) based on tiers
Sell: MACD spread > z score threshold (overbought) based on tiers
When overbought, do not buy until oversold (see tier table below)
At Time = 0, hold Portfolio at 100% USD until oversold then buy into BTC accordingly

Z score example	Min	Max	BTC	USD
Extreme Overbought	3	N/A	0.05	0.95
Overbought	2	3	0.2	0.8
Slight Overbought	1	2	0.35	0.65
Neutral	-1	1	0.5	0.5
Slight Oversold	-2	-1	0.65	0.35
Oversold	-3	-2	0.8	0.2
Extreme Oversold	N/A	-3	0.95	0.05

2.2. Analysis¶

First we observe from the '26dma MACD spread btc' plot that MACD SMA spread is less volatile than BTC spread over the same period, resulting in less portfolio rebalancing. This is expected given MACD spread applies smoothing to BTC price three times: in creating MACD line (12dma - 26dma), in creating the signal line (9dma MACD line), and finally in the 26dma spread of the MACD/Signal difference. The result is likely lower risk than holding BTC.

Second we see that the MACD spread visibly diverges from the BTC spread. Although lower risk, the risk-adjusted returns might underperform if the portfolio returns fail to make up the difference.

3. Run Strategy¶

3.1. Portfolio Rebalancing¶

The rebalancing is calculated as follows: the signal at the end of previous day informs next day's portfolio distribution. For example, hypothetically at the end of 01-31-2021, we have a Z score of -2.5. The portfolio distributes 80% of current value to BTC, 20% to USD. On 02-01-2021, 80% of portfolio value from 01-31-2021 is subjected to 02-01-2021's BTC return for the day.

Calculations:
$V_T$ = portfolio value at time T
$P_T$ = proportion of BTC in the portfolio
$R_T$ = BTC daily simple returns

$$V_T = V_{T-1} * P_{T-1} * R_T$$

3.2. Analysis¶

The strategy sells BTC to 5% during three major periods and holds it in 0.05/0.95 BTC/USD ratio:

2011-Nov to 2012-Jan
2016-Jun to 2017-Jul
2020-Sep to 2020-Dec

During those periods, the graph shows the strategy could not take advantage of bull runs, in the particular the 2017 exponential bull run when price quadripled.

4. Performance Summary¶

4.1 Calculate Performance¶

We calculate the annualized Sharpe, Sortino, and Information ratio as follows:

$$Sharpe =\sqrt365 \ * \frac{\bar{R_p} - R_f}{\sigma_p}$$$$Sortino = \sqrt365 \ * \frac{\bar{R_p} - R_f}{\sigma_{downside \ risk}}$$$$Information = \sqrt365 \ * \frac{\bar{R_p} - \bar{R_h}}{\sigma_{tracking \ error}}$$

Where:

$$\bar{R_p} = mean(ln(\frac{R_{p,n}}{R_{p,n-1}}))$$$$\sigma_p = std(ln(\frac{R_{p,n}}{R_{p,n-1}}))$$$$\sigma_{downside \ risk} = std(ln(\frac{R_{p,n}}{R_{p,n-1}} < 0))$$$$\sigma_{tracking \ error} = std(ln(\frac{R_{p,n}}{R_{p,n-1}} - ln(\frac{R_{h,n}}{R_{h,n-1}}))$$

We use log returns instead of simple returns due averaging returns over multiple periods. Simple returns would have returned inflated ratios. We multiply by square root of 365 given our average mean returns is calculated on a daily basis, and BTC trades 24/7/.

4.2. Analysis¶

On an annualized basis, MACD SMA spread fails to outperform holding BTC in a risk-adjusted basis for all performance ratios across 1mo, 3mo, 6mo, 12mo, 24mo, and 36mo trailing periods. We see from the trailing returns and volatility plots that despite the portfolio halving volatility, it missed significant periods of high returns, which was likely a culprit for its underperformance.

This analysis is weak evidence against our hypothesis that MACD spreads beats holding BTC. Several factors mentioned at the start contributed to this performance, such as using SMA instead of EMA, and the difficulty of annualizing ratios. In fact, for the past 365 days, although MACD underperformed BTC, the actual results are:

MACD ret: -34%
BTC ret: -48%
MACD vol: 0.02
BTC vol: 0.04

On this non-annualized basis, MACD portfolio outperforms holding BTC. Next steps could be to give alternative performance indicators to capture these results.